The present invention relates generally to the field of fluid flow measurement, and more particularly to a method and system for determining flow rates and/or fluid density in single and multiple-phase flows utilizing discharge coefficient relationships.
Obstruction flow meters, such as orifices, venturi meters, and v-cones, are used to measure flow rates of fluids having one or more phases. Flow meters are calibrated to obtain a discharge coefficient, which is the ratio of actual flow rate to theoretical flow rate. Discharge coefficient equations are experimentally determined for obstruction flow meters. The equations obtained for use in calculating the discharge coefficient are complex and dependent upon the Reynolds number, pipe diameter, and xcex2 ratio. Based on available data, the discharge coefficient may vary significantly with Reynolds number and pipe diameter. The complexity of the equations may lead to confusion and difficulty in the evaluation of the discharge coefficients since different terms must be discarded at different xcex2 ratios.
According to one embodiment of the invention, a computerized method for determining a flow rate of a fluid flowing through a conduit having an obstruction flow meter includes receiving a xcex2 ratio value indicative of a xcex2 ratio of the obstruction flow meter, receiving a pressure differential value indicative of a pressure differential across the obstruction flow meter, receiving a density value indicative of a density of the fluid, receiving a discharge coefficient formula for the obstruction flow meter, the discharge coefficient formula being a function of the xcex2 ratio of the obstruction flow meter and an Euler number for the fluid flowing through the conduit, and determining, by the computer, the flow rate based on the received xcex2 ratio value, the received pressure differential value, the received density value, and the received discharge coefficient formula. The determined flow rate may either be the volumetric flow rate or the mass flow rate.
According to another embodiment of the invention, a computerized method for determining a density of a fluid flowing through a conduit having an obstruction flow meter includes receiving a xcex2 ratio value indicative of a xcex2 ratio of the obstruction flow meter, receiving a pressure differential value indicative of a pressure differential across the obstruction flow meter, receiving a flow rate value indicative of a flow rate of the fluid, receiving a discharge coefficient formula for the obstruction flow meter, the discharge coefficient formula being a function of the xcex2 ratio of the obstruction flow meter and an Euler number for the fluid flowing through the conduit, and determining, by the computer, the density based on the received xcex2 ratio value, the received pressure differential value, the received flow rate value, and the received discharge coefficient formula. The received flow rate may either be the volumetric flow rate or the mass flow rate.
According to an additional embodiment of the invention, a computerized method for determining a discharge coefficient formula for an obstruction flow meter coupled to a conduit includes receiving a plurality of first, second, and third data points, the first data points indicative of a measured discharge coefficient of the obstruction flow meter, the second data points indicative of an Euler number for a fluid flowing through the conduit, and the third data points indicative of a xcex2 ratio of the obstruction flow meter, and determining, by the computer, the discharge coefficient formula for the obstruction flow meter from the first, second, and third data points, the discharge coefficient formula a function of the Euler number and the xcex2 ratio.
Embodiments of the invention provide a number of technical advantages. Embodiments of the invention may include all, some, or none of these advantages. Defined relationships between applicable flow variables are easier to curve fit than traditional relationships, which allows more accurate calculation of discharge coefficient equations. New discharge coefficient relationships eliminate the need to know fluid viscosity, which increases the accuracy of flow rate calculations by eliminating the uncertainty of viscosity. In addition, eliminating viscosity and pipe diameter when determining a calibration curve equation simplifies these equations and, as a result, reduces the computing power necessary for flow rate measurements. New discharge coefficient relationships developed may be used for single and multiple-phase flows.